An adaptive speed control that emits a radar beam and detects a preceding vehicle based on the reflected and received partial waves is known from the publication “Adaptive Cruise Control System Aspects and Development Trends” by Winner, Witte, Uhler and Lichtenberg, published at the SAE International Congress & Exposition, Detroit, Feb. 26-29, 1996. If this adaptive speed control detects a preceding vehicle, the speed of the vehicle is controlled in terms of a constant distance control and the preceding vehicle is followed. If the radar sensor detects that there is no preceding vehicle, the speed control regulates the speed of the vehicle in terms of constant speed control to a speed input set by the driver. It is also described that the distance of the vehicle from the preceding vehicle is able to be set in the form of a time gap. In this context, the time gap represents the time period that the driver's own vehicle requires to cover the intermediate vehicle distance. This results in a speed-dependent distance based on the natural driving behavior of a human driver.